This invention relates to analog computation circuits and more particularly to circuits and methods for designing and using analog circuits operating in the modulation domain.
Instrumentation systems sometimes require the generation of a time-varying signal that is the ratio of two other signals. This may be accomplished either with an analog divider computation circuit or it may be done by digitizing the two input signals and using numerical computation, commonly known as Digital Signal Processing (DSP). Digital techniques are limited to relatively low frequencies because of the intense computation load placed on the processor. Analog division can potentially have greater bandwidth, but is difficult to implement using conventional techniques.
A commonly used circuit and method to perform the division using logarithms is shown in FIG. 5. This circuit is based on the mathematical property that the logarithm of a quotient is equal to the difference of the logarithms of the dividend and divisor.
As shown in FIG. 5, input signals n(t) and d(t) to circuit 50 are conditioned by passing each of them through logarithm function blocks 501 and 502 respectively. The logarithms of the input signals are subtracted by block 503 and the result is sent to anti-logarithm (exponentiation) block 504. The accuracy of nonlinear circuit 50 depends upon how accurately the logarithmic (501, 502) and antilogarithmic (504) functions are realized. If the signals involved have wide dynamic range, then the transistors within the calculation blocks must operate over a wide range of currents. This increases the difficulty of achieving accurate nonlinear functions. Also, when the current is small, bandwidth tends to suffer. The design equations for this type of circuit are all highly temperature dependent, making drift a problem. It is also difficult to obtain a low noise floor using analog circuits as described.
Another commonly used circuit and method is to use a multiplier, such as multiplier 602, in a feedback path of a servo loop, as shown in FIG. 6 circuit 60. This has the effect of using a multiplier to obtain division when its output is fed into subtractor 601. Such a circuit is an inverse multiplier analog divider. Multiplier 602 is commonly constructed as a Gilbert multiplier. There are two main practical difficulties with this circuit. First the divider accuracy can be no better than the accuracy of the multiplier. Although a Gilbert multiplier is somewhat easier to build than the logarithmic circuits of FIG. 5, it still has problems with linearity, dynamic range, and noise. Second, the accuracy of the circuit is also affected by errors in the servo loop. Impairments in servo amplifier 603 can cause loop tracking errors, denoted xcex5 in FIG. 6. Also, the loop gain varies depending on the characteristics of the signals being divided. This makes loop design difficult and loop dynamics unpredictable.
FIG. 7 shows Armstrong phase modulator 70 where sine wave carrier generator 701 drives multiplier 703 via amplifier 705 (gain xe2x88x921) which is being used as a double side band suppressed carrier (DSB-SC) (balanced) modulator. A DSB-SC signal is the same as a conventional amplitude modulation signal, except that the carrier is suppressed. Modulation input port 710 drives the other input of multiplier 703. The output of multiplier 703 is a DSB-SC signal. The DSB-SC signal drives one input of adder 704. The other input to the adder is the carrier signal shifted 90xc2x0 by shifter 702. Output 711 of adder 704 is a phase-modulated signal. The modulation index is proportional to the ratio of the amplitude of the DSB-SC signal to the injected carrier amplitude. Modulation index is defined as the peak phase deviation in radians.
For proper operation, the maximum modulation index must be within the xe2x80x9csmall angle approximationxe2x80x9d regime, where phase modulation can be considered a linear process. This is also known as narrow band phase modulation (NBPM). In general, phase modulation (a member of the angle modulation family) is a non-linear process. The modulation index limit for NBPM is approximately 0.5, depending on the amount of modulation error that can be tolerated. For example, if the modulation index is limited to 0.45, then the harmonic distortion for tone modulation is less than 5%.
The present invention is directed to a system and method for performing analog division in the modulation domain. In one embodiment of the invention, a sine wave carrier is modulated by one of the input signals and a cosine wave carrier is modulated by the other of the input signals. These modulated signals are added together with the result being a modulated signal having a phase modulation index proportional to the ratio of the amplitudes of the first and the second input signals. This signal is then phase demodulated. The resulting baseband signal is proportional to the ratio of said first to said second signals.
The foregoing has outlined rather broadly the features and technical advantages of the present invention in order that the detailed description of the invention that follows may be better understood. Additional features and advantages of the invention will be described hereinafter which form the subject of the claims of the invention. It should be appreciated by those skilled in the art that the conception and specific embodiment disclosed may be readily utilized as a basis for modifying or designing other structures for carrying out the same purposes of the present invention. It should also be realized by those skilled in the art that such equivalent constructions do not depart from the spirit and scope of the invention as set forth in the appended claims. The novel features which are believed to be characteristic of the invention, both as to its organization and method of operation, together with further objects and advantages will be better understood from the following description when considered in connection with the accompanying figures. It is to be expressly understood, however, that each of the figures is provided for the purpose of illustration and description only and is not intended as a definition of the limits of the present invention.